Diagnosis of linear programming supply chain optimization models: Detecting infeasibilities and minimizing changes for new parameter values. (March 2023)

• Record Type: Journal Article
• Authors: Jatty, Sitoshna; Singh, Niharika; Grossmann, Ignacio E.; de Assis, Leonardo Salsano; Galanopoulos, Christos; Garcia-Herreros, Pablo; Springub, Bianca; Tran, Nga
• Is Part Of: Computers & chemical engineering. Volume 171(2023)
• Publication Date: 2023-03
• Subjects: Supply chain -- Disruptions -- Infeasibility diagnosis -- Flexibility test -- Time-series model -- Bi-objective optimization; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2023.108139
• Languages: English
• ISSNs: 0098-1354

Abstract

Abstract: In this paper, we address two major challenges in linear programming supply chain models: detecting infeasibilities and minimizing changes when new parameter data are introduced in the model. First, we address the problem of detecting and restoring feasibility using the flexibility test method to quantitatively evaluate the constraints in the model that are causing infeasibility. If the parameters in these infeasible constraints were incorrectly specified, we use regression and time-series models to detect outliers in the data that may be the cause of infeasibility. Corrective actions may be taken by the user upon identification of the cause of infeasibility through this algorithm. Second, we address the problem of minimizing changes in the solution of the linear programming model that are introduced due to varying parameters. The three formulations minimize the magnitude of changes, number of changes, and the weighted sum of both magnitude and number of changes in the model. We also formulate a bi-criterion optimization model to consider the objectives of minimizing cost and minimizing the weighted sum of the number and magnitude of changes to analyze the trade-off between the two objectives. An ideal compromise solution between the two objectives is also presented. The proposed algorithms are applied to supply chain problems including real industrial problems, to demonstrate their usefulness. Highlights: Detecting infeasibilities in LP supply chain models is performed with the flexibility test method. To detect outliers of parameters incorrectly entered a machine learning technique. Minimizing magnitude and number changes, and weighted sum when changing parameters in LP mode. Bi-criterion optimization minimizes cost and weighted sum of the number and magnitude changes. Algorithms applied to several supply chain test problems to demonstrate their usefulness.